Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5827 | C2 | semidirect |
| 3. C2×C3×#104 | C2 | semidirect |
| 4. #5131 | C2 | semidirect |
| 5. #4939 | C2 | semidirect |
| 6. #4554 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 14. #949 | C4 | semidirect |
| 31. C2×#104 | D3 | semidirect |
| 54. C2×D12 | C2×C4 | semidirect |
| 73. #208 | C2×C4 | semidirect |
| 103. C3×Q8 | C22⋊C4 | semidirect |
| 107. C3×D4 | C22⋊C4 | semidirect |
| 200. Q8 | (C2×D3)⋊C4 | semidirect |
| 208. D4 | (C2×D3)⋊C4 | semidirect |
| 257. C3 | #1883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5827 | 2 |
| C2×#949 | 2 |
| C2×C3×#104 | 2 |
| #5131 | 2 |
| #4939 | 2 |
| #4554 | 2 |
| #4523 | 2 |
| #1883 | 3 |